Structure & Representations of Jordan Algebras (Colloquium Publications) by Nathan Jacobson
English | 2008 | ISBN: 082184640X | 453 Pages | DJVU | 7 MB
The theory of Jordan algebras has played important roles behind the scenes of several areas of mathematics. Jacobson's book has long been the definitive treatment of the subject.
It covers foundational material, structure theory, & representation theory for Jordan algebras. Of course, there are immediate connections with Lie algebras, which Jacobson details in Chapter 8. Of particular continuing interest is the discussion of exceptional Jordan algebras, which serve to explain the exceptional Lie algebras & Lie groups. Jordan algebras originally arose in the attempts by Jordan, von Neumann, & Wigner to formulate the foundations of quantum mechanics. They are still useful & important in modern mathematical physics, as well as in Lie theory, geometry, & certain areas of analysis.
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